Nuclear magnetic resonance (NMR) is used as a tool in a number of different technology areas to investigate different types of medium. NMR can occur when the medium is subjected to a static magnetic field and to an oscillating magnetic field. When subjected to an applied static magnetic field, polarization of nuclear magnetic spins of the medium occurs based on spin number of the medium. Applying an electromagnetic field to the medium in the static magnetic field can perturb the polarization established by the static magnetic field. In typical measurements, the static magnetic field and the perturbing field are perpendicular to each other. Collected responses received from the medium related to the total magnetization of nuclear spins in the medium, in response to these applied fields, can be used to investigate properties of the medium, and may provide imaging of the medium.
Nuclear magnetic resonance measurements are created by the oscillation of excited nuclear magnetic spins in the transverse plane, that is, the direction perpendicular to the magnetic field. This oscillation eventually dies out and the equilibrium magnetization returns. The return process is referred to as longitudinal relaxation. The time constant, T1, for nuclei to return to their equilibrium magnetization Mo is called the longitudinal relaxation time or the spin lattice relaxation time. The magnetization dephasing, that is losing coherence, along the transverse plane is given the time constant T2 and is called the spin-spin relaxation time. The loss of phase coherence can be caused by several factors including interactions between spins or magnetic gradients.
A widely used NMR measurement technique, referred to as CPMG (in view of its designers Carr, Purcell, Meiboom, and Gill), uses a sequence of radio frequency pulses to produce spin echoes and counteract dephasing of the magnetization in the medium investigated. In the CPMG sequence, an initial pulse, commonly a 90° pulse, can be applied to tip the polarization into a plane perpendicular to the static magnetic field. To counter dephasing due to magnetic inhomogeneities, another pulse, a recovery pulse, is applied to return to phase, which produces a signal called an echo from the medium. Yet, after each return to phase, dephasing begins and another recovery pulse is applied for rephasing. Rephasing or refocusing is repeated many times in the CPMG sequence, while measuring each echo. The echo magnitude decreases with time due to a number of irreversible relaxation mechanisms. The CPMG sequence can have any number of echoes, where the time between each echo can be relatively short, for example, of the order of 1 ms or less or as long as 12 ms is used.
FIG. 1 illustrates use of a 90° tipping pulse and a sequence of 180° refocusing pulses. In this sequence, the ten 180° refocusing pulses cause ten echoes, where the peak amplitudes of the echoes are equally spaced apart by a peak to peak time distance, TE, that corresponds to the equally spaced apart time distances of the refocusing pulses. Also indicated is an acquisition window for capturing the signal of an echo. The echoes decay due to dephasing according to T2 for the medium. Once the nuclear spin population is fully recovered for the sequence, the medium can be probed again by another sequence.
Petrophysical information can be derived from NMR measurements, such as, but not limited to petrophysical properties of fluid containing porous media. Various properties that can be measured using an NMR tool include pore size, porosity, surface-to-volume ratio, formation permeability, and capillary pressure. For instance, the distribution of T2 values can be used to estimate pore size. As noted above, T2 is related to loss of phase coherence that occurs among spins, which can be caused by several factors. For example, magnetic field gradients in pores lead to different decay rates. Thereby different pore sizes in the formation produce a distribution of T2 values, which is shown in the conversion of spin-echo decay data of NMR measurements. This distribution represents a “most likely” distribution of T2 values that produce the echo train of the measurement. This distribution can be correlated with a pore size distribution when the rock is 100% water saturated. However, if hydrocarbons are present, the T2 distribution will be altered depending on the hydrocarbon type, viscosity, and saturation. With proper calibration and account for hydrogen index of the fluids in the pore space, the area under a T2 distribution curve is equal to total porosity. More precision in the evaluation of NMR data may be aided with increased acquisition of data from multiple NMR measurements.